Question: Reduce to lowest terms: $ \dfrac{1}{2} \div \dfrac{5}{7} = {?}$
Dividing by a fraction is the same as multiplying by the reciprocal of the fraction. The reciprocal of $ \dfrac{5}{7}$ is $ \dfrac{7}{5}$ Therefore: $ \dfrac{1}{2} \div \dfrac{5}{7} = \dfrac{1}{2} \times \dfrac{7}{5} $ $ \phantom{ \dfrac{1}{2} \times \dfrac{7}{5}} = \dfrac{1 \times 7}{2 \times 5} $ $ \phantom{ \dfrac{1}{2} \times \dfrac{7}{5}} = \dfrac{7}{10} $